Weighted extensions of generalized cumulative residual entropy and their applications

Abstract

In this paper, we consider weighted extensions of generalized cumulative residual entropy and its dynamic(residual) version. Our results include linear transformations, stochastic ordering, bounds, aging class properties and some relationships with other reliability concepts. We also define the conditional weighted generalized cumulative residual entropy and discuss some properties of its. For these concepts, we obtain some characterization results under some assumptions. Finally, we provide an estimator of the new information measure using empirical approach. In addition, we study large sample properties of this estimator.